Australian Curriculum Mathematics/General Mathematics

Matrix Addition

$\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 1\\ 1& 0& 1\end{array}\right]+\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 0\\ 1& 1& 1\end{array}\right]=\left[\begin{array}{ccc}0& 1& 2\\ 1& 1& 1\\ 2& 1& 2\end{array}\right]$

$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]+\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]=\left[\begin{array}{cc}a+p& b+q\\ c+r& d+s\end{array}\right]$

Matrix Multiplication

$A\times I=I\times A=A$

$A\times I=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\times \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1\times a+0\times b& 0\times a+1\times b\\ 1\times c+0\times d& 0\times c+1\times d\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=A$

$\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 1\\ 1& 0& 1\end{array}\right]+\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 0\\ 1& 1& 1\end{array}\right]=\left[\begin{array}{ccc}0& 1& 2\\ 1& 1& 1\\ 2& 1& 2\end{array}\right]$